摘要
随着工程系统问题的复杂性和不确定因素的逐渐增加,可靠性日益成为科学和工程中的一个重要概念和保证工程系统功能稳定的主要质量指标。传统的基于概率(随机)可靠性理论的设计、分析方法是目前用于不确定性处理的最为常用和成功的方法。但对于结构复杂、工作条件经常改变的机械系统(如大型起重运输机械),往往较难或无法获得足够的统计数据,且初始数据通常包含着大量的主观信息和认知不确定性(Epistemic uncertainty)。由于这类系统通常具有多发性故障、多故障模式等特点,适用于设计初期的可靠性数据可信性不大。传统的概率可靠性方法对已知数据的依赖性较强,计算或分析结果往往跟实际情况偏差较大。
本文在国家自然科学基金项目资助下,针对概率可靠性方法在理论和应用上的若干局限性,以及机械装备设计中常常出现的数据不足及数据具有模糊性的实际情况,基于融合可能性理论模型和可能性计算方法的可能性度量(Possibilistic measurements)体系,研究信息不完善条件下复杂机械系统的可靠性分析和评价问题。
研究工作目的之一是探索基于可能性度量方式的系统可靠性分析的新理论和新方法；其次,为系统非概率可靠性分析建立基于“不确定形式规范化一测度与积分量化一应用方法研究”流程的设计框架；最后为提高统计数据缺乏时机械装备的可能可靠性设计水平和可能可靠性管理水平提供技术支撑与技术保障。
结合模型研究和方法开发,结合定性分析和定量计算,论文研究的主要工作如下：
(1)研究可靠性设计和分析中不确定性的认知属性及其处理问题。剖析机械系统和结构可靠性分析中涉及基本输入、可靠性模型、度量手段以及外部操作环境等多方面来源的不确定因素及其实质,给出实际可靠性工程中数据不足现象的表现、特征及其认知不确定性本质。比较在概率体系和非概率体系框架下,可靠性中不确定性解决方案的不同度量方式,进而说明随机可靠性模型中特征参数、分布类型、样本容量和先验分布等因素对模型偏差的较大影响。提供认知不确定性在表达、合成和传播上的主要方式,为可靠性分析中不确定因素的处理提供必要的理论基础框架。
(2)研究可能不确定性及其相应信息的度量问题。通过可能不确定性命题对应的信息类型和语义解释,说明可能性度量方式的测度二元性(可能性测度和必要性测度)和量化双极性(乐观标准和悲观标准)特点在刻画认知不确定性时的计算实现。通过可能性理论与概率论和模糊集合论在公理背景、模型表达和运算特点等方面的比较研究,给出可能性度量方式在相关理论中的测度转化形式。接着探讨建造可能性分布函数的隶属函数生成法和概率分布转化法。以此为基础,通过对少量客观数据进行主观赋值,给出在可能可靠性理论建模中基于可能性中值的可能性分布构造方法,并对齿轮弯曲疲劳强度试验中的寿命分布进行实例分析,建立数据不足时基于可能性方法的系统分析和可靠性设计的测度与积分框架。
(3)研究基于可能性度量的可能可靠性建模问题。以可能性测度取代概率测度刻画系统(元部件)的失效行为,将寿命视为可能性空间上的模糊变量。通过拓宽系统寿命的定义域,在不影响问题本质的前提下简化能双(Posbist)可靠性模型的推导,实现包括串联、并联、串并联混合系统、冷储备系统等在内的典型系统Posbist可靠度计算。通过可能可靠性与概率可靠性的对比分析实例,说明认知不确定性在可靠性一般系统模型中的度量方法,建立数据不足条件下结合可能性方法与系统可靠性分析的一般模型框架。
(4)研究对应典型系统可能可靠模型的故障树分析和重要度分析问题。一方面,从故障角度采用可能性测度刻画系统中状态变量的可能不确定属性,重新定义单调关联系统和可能性故障树的结构函数,建立基于能双相干系统的故障树模型并推导适用于定性分析的最小割集(MCs)模型和适用于定量分析的逻辑门的可能性算子。另一方面,结合可能性理论的自然语言处理能力和广义信息论对非可加性测度的引申,建立基于可能性信息熵的重要性测度模型及分析方法。通过基于集合论和测度论的二维模型框架,定义可能性空间上公理化的重要度指标。通过重要性事件的识别实例对认知不确定性的敏感性分析问题进行探索,构建一种适合实际可靠性分析的应用方法。
综合以上工作,在起重机械结构方案选型、起重机钢丝绳断绳事故分析、起重机危险因素分析以及安全综合评价等工程实例中验证本文研究结果,得出以下结论,即认知不确定性描述对于数据不足现象处理的适应性、可能不确定度量对于认知不确定处理的有效性,以及可能可靠性系统模型与故障树模型对于可能性度量方法应用于可靠性分析和安全评价等工程实际的可行性。
本文的研究可望推广应用于其它多种复杂设备的可靠性综合评估、故障检测和安全控制中。
With an ever-increasing tendency to take uncertainty factors into account in engineering design, reliability has now been an important concept in science and engineering as well as a primary quality index of guaranteeing stable performances. The traditional stochastic/ probabilistic reliability method is a successful tool to handling uncertainty and has been widely used in engineering. Yet considering complex mechanical systems with frequently variant working conditions (e.g. crane and transporter), necessary statistic data is often not available, and there exist vast subjective information and epistemic uncertainty in initial data. Due to the frequent faults and multiple fault modes of such mechanical systems, their reliability data is thus different according to the adopted statistical approach. Moreover, the reliability data is also variant according to different types of mechanical system, which leads to lack of data or limited belief in preliminary design. The stochastic method is strongly depends upon the available information, which greatly restricts its applications in engineering.
Against the backgrounds of the NSFC project, in consideration of some drawbacks of stochastic reliability method in theory and applications, as well as the existence of insufficient and vague data in actual equipments design, the reliability analysis and evaluation problems of complex mechanical systems are investigated in this dissertation, by means of possibilistic measurements integrating possibilistic theoretical models and operational methodologies.
The purpose of this study includes three aspects. First of all, it attempts to explore new reliability theories and methodologies in the context of possibility theory and measurement. Secondly, it attempts to build up a design framework from uncertainty formalization to integral/measure qualification, and then to application methodologies. Thirdly, it attempts to provide some technical supports and guarantees for possibilistic reliability design and possibilistic reliability management in the case of limited statistical data.
In combination with theoretical research and methodological exploitation, and integrating qualitative analysis with quantitative computations, the dissertation includes the following contributions:
(1) The representation, synthesize and qualification of epistemic uncertainty in reliability design and analysis are investigated when necessary statistical data is scarce. Starting with a holistic understanding of uncertainty, uncertainty factors inherent in reliability inputs, reliability models, reliability inferences and external operating environments are analyzed in detail to find out their essences, and then the behaviors and appearances of insufficient data in reliability engineering are presented, which reveal the handling of epistemic uncertainty plays an important role in reliability analysis with imprecise or incomplete parameters. After comparing probabilistic approach with non-probabilistic approach in reliability design, some vital factors in model errors such as character parameters, distribution types, sample capacities and prior distributions are pointed out in turn, which provides a theoretical background for uncertainty formalization and validation in reliability analysis.
(2) The measurements of possibilistic uncertainty and its corresponding information are studied. With an explanation of information types and information semantic of possibilistic uncertainty, the duality of possibility measure and necessity measure, as well as the bipolarity of optimistic criterion and pessimistic criterion are explored for epistemic uncertainty validation computationally. By a comparative analysis of possibility theory with some relative theories, the connections and transformations between them are proposed. Then two approaches to constructions of possibility distributions are provided, respectively as possibility distribution generations based on membership functions and possibility distribution transformations from probability distribution. Especially, when there is limited objective reliability data, a new method of developing the possibility distribution by subjective assignment strategy is put forward, which makes use of the concept of interval-valued possibilistic mean value of a L-R fuzzy number and is then illustrated by the lifetime data from fatigue reliability tests. These works provide a possibilistic design framework on the measure and integral background.
(3) The possbilistic reliability models of typically general systems are constructed. Characterizing the systems(components) failure behavior by possibility measures in place of probability measures, treating the systems (components) lifetime as fuzzy variables in the possibility space, and introducing possibilistic approaches into system reliability modeling and analysis, the possibilistic reliability theories are advanced based on possibilistic measurements. By expanding the universe of discourse, the derivation of Posbist reliability models is simplified without loss of the nature of the problems to be solved, and the proofs and calculations of Posbist reliability of typical systems including series, parallel, series-parallel, parallel-series, and cold standby systems are much more straightforward. The detailed application examples in system reliability analysis provide a possibilistic design framework on the general reliability models background.
(4) The models of possibilistic FTA and the approach to possibilistic importance analysis in accord with possibilistic reliability theory are exploited. From one side, a Posbist fault tree model of coherent systems is constructed by means of possibilistic characterizations of state variables from the viewpoint of fault, along with redefinitions of structure functions of coherent systems and possibilistic fault tree. The MCS model for qualitative analysis and possibilistic operators of logic gates for quantitative analysis are then proposed, respectively. They are suitable for predicting and diagnosing failures and evaluating reliability and safety of systems, in which the statistical data is scarce or the failure probability is extremely small. From another side, combining the ability of possibility theory in handling natural language with the extension of non-addictive measures by GIT, a new importance measure is proposed based upon possibilistic information entropy. In a two-dimensional framework combining both the set theory and the measure theory, an axiomatic index of importance is defined in the possibility space and then the modeling principles are presented after investigating the possibilistic information semantics, measure-theoretic terms and entropy-like models. Not only uncertainty quantification but also sensitivity analysis of possibilistic uncertainty is concerned in this study, which provide a practical methodology on the reliability application background.
From the above works, with the engineering application of the concept selection for mechanical systems, fault tree analysis of the crane rope and a comprehensive safety evaluation of crane machinery, our conclusions could be summarized as follows, i.e. the adjustability of epistemic uncertainty characterizations for the occurrences of insufficient data, the effectiveness of possibilistic measurements for the handling of epistemic uncertainty, and the feasibility of possibilistic system models and fault tree models for the application of possibilistic measurements in reliability analysis.
In this dissertation, the proposed models and methodologies would be extended to applications in the overall reliability evaluations, fault diagnosis and safety control of other complex engineering machinery.
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